In general, LKH ([1]} [1]}) uses \(\alpha \) -measure and \(\pi \) -values to improve the performance of LK. Moreover, the iteration of \(k\) -opt process in LKH will stop immediately if a \(k\) -opt move is found that can improve the current TSP tour. And LKH uses a 5-opt move as the basic move, which means the maximum value of \(k\)  in the \(k\) -opt process of LKH is 5.
